Medical problem solving can be aided by computer graphic displays that support sound mental models. The mental models approach is distinguished from expert systems and decision analysis in several ways. Mental models go beyond procedures and rules in that they are mental representations that act as simpler analogues of complex real world target systems. Further, mental models are concrete systems with discrete internal mechanisms, and so support and encourage mental simulation for testing and developing hypotheses about the target system. Finally, mental models can have useful unplanned properties, and thus can lead to unexpected new discoveries. Formation of a good mental model for thinking about a medical problem is not always easy. This is especially true in situations where several variables are simultaneously acting on the target system. Bayesian inference provides one notorious example of a system for which a clear mental model is difficult to form, and is therefore one promising area where mental model support could measurably improve physician decision making. Patient monitoring during mechanical ventilation is proposed as a second area where complex multivariate data can be represented in elegant, interactive graphic displays, and so support good mental modelling. Prototype graphic systems are described for aiding diagnostic inference and ventilator monitoring. Psychology experiments are described to (a) investigate the psychological impact of these graphic displays on the use of mental models in medical problem solving and (b) develop the prototype graphic systems into finished products. Investigation of psychological impact includes research to determine show what sort of decisions these graphic displays promote, what sort of mental models they support, and how they affect accuracy, efficiency, and confidence.